This question could mean a couple things, and people's answers are a bit different.
First, like ronne said, there is a message that pops up saying that things will change, every time you transition to a new act, so if you ran through the Act 1 Underdark all the way until you got the message that moving on will change things, then the act 1 Underdark is done (if you didn't clear all the Act 1 Underdark, then things may have changed when you moved to the mountain pass). The act 2 "Underdark" is named something different, but is still in the Underdark, and you should be able to access it from the act 2 topside map, if the boat in act 1 doesn't work for some reason. Dunno how it changes the story you experience, if you enter the Act 2 "Underdark" area from the top.
Same applies to the mountain pass, as Grabbit said, you can access it from the act 2 side, if you took the Underdark boat to transition from act 1 to act 2.
Act 2 areas that I know of (multi-part spoiler, in order of how you find them): Underdark pt.2, Mountan Pass, the Valley of Moonrise Tower, and a Tomb (dont want to spoil anything more about it).